2012/05/30 by Mansour, Hassan, Yilmaz, Ozgur
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1205.6845
In this paper, we study the support recovery conditions of weighted ℓ1 minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from ℓ1 minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted ℓ1 minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted, ℓ1 minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.